TECHNICAL NOTE DATA QUALITY
INTRODUCTION
1 Estimates in this publication are based on information obtained from occupants of a sample of dwellings, and are subject to sampling variability. That is, they may differ from those estimates that would have been produced if all dwellings had been included in the survey. One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of dwellings was included. There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all dwellings had been included, and about 19 chances in 20 (95%) that the difference will be less than two SEs. Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate.
2 Due to space limitations, it is impractical to print the SE of each estimate in the publication. Instead, a table of SEs is provided to determine the SE for an estimate from the size of that estimate (see table T1). The SE table is derived from a mathematical model, referred to as the 'SE model', which is created using data from a number of past Labour Force Surveys. It should be noted that the SE model only gives an approximate value for the SE for any particular estimate, since there is some minor variation between SEs for different estimates of the same size.
CALCULATION OF STANDARD ERROR
3 An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Table 10 shows that 435,600 people involuntarily ceased a job during the year and their duration in that job was less than 12 months. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 6,650 and 8,350 and can be approximated by interpolation using the following general formula:
4 Therefore, there are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall within the range 427,800 to 443,400 and about 19 chances in 20 that the value will fall within the range 420,000 to 451,200. This example is illustrated in the following diagram.
r
5 In general, the size of the SE increases as the size of the estimate increases. Conversely, the RSE decreases as the size of the estimate increases. Very small estimates are thus subject to such high RSEs that their value for most practical purposes is unreliable. In the tables in this publication, only estimates with RSEs of 25% or less are considered reliable for most purposes. Estimates with RSEs greater than 25% but less than or equal to 50% are preceded by an asterisk (e.g.*3.2) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs of greater than 50%, preceded by a double asterisk (e.g.**0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of less than 25%.
PROPORTIONS AND PERCENTAGES
6 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y.
7 Considering the previous example from table 10, of the 435,600 people who ceased a job involuntarily during the year ending February 2010, and their duration of last job was less than 12 months, 242,300 or 55.6% gave their reason as 'Job was temporary or seasonal'. The SE of 242,300 may be calculated by interpolation as 6,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 6,000/242,300 = 2.5%. The SE for 435,600 was calculated previously as 7,800, which converted to an RSE 7,800/435,600=1.8%. Applying the above formula, the RSE of the proportion is:
8 Therefore, the SE for the proportion of people who reported their reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was less than 12 months is 0.9 percentage points (=(55.6/100)x1.7). Therefore, there are about two chances in three that the proportion of people who reported their reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was less than 12 months or more was between 54.7% and 56.5% and 19 chances in 20 that the proportion is within the range 53.8% to 57.4%.
DIFFERENCES
9 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or percentages). Such an estimate is subject to sampling error. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (xy) may be calculated by the following formula:
10 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
STANDARD ERRORS
T1 STANDARD ERRORS OF ESTIMATES 

         AUST. 
 NSW  Vic.  Qld.  SA  WA  Tas.  NT  ACT  SE  RSE 
Size of Estimate (persons)  no.  no.  no.  no.  no.  no.  no.  no.  no.  % 

100  290  290  220  180  220  110  80  100  110  110.0 
200  400  380  320  240  290  160  120  170  190  95.0 
300  470  440  390  280  340  190  150  210  260  86.7 
500  580  540  500  340  420  240  190  270  380  76.0 
700  660  620  580  390  480  270  220  300  480  68.6 
1,000  760  710  680  450  550  310  260  330  610  61.0 
1,500  900  830  810  530  640  360  300  360  780  52.0 
2,000  1 010  930  910  590  710  390  330  390  920  46.0 
2,500  1 100  1 000  1 000  650  800  400  350  400  1 050  42.0 
3,000  1 200  1 100  1 050  700  850  450  400  450  1 150  38.3 
3,500  1 250  1 150  1 100  700  900  450  400  450  1 250  35.7 
4,000  1 300  1 200  1 200  750  900  500  400  450  1 350  33.8 
5,000  1 450  1 300  1 250  800  1 000  500  450  500  1 500  30.0 
7,000  1 650  1 500  1 450  900  1 150  600  550  600  1 700  24.3 
10,000  1 850  1 700  1 600  1 050  1 300  700  700  700  2 000  20.0 
15,000  2 150  1 950  1 800  1 200  1 500  850  1 000  850  2 350  15.7 
20,000  2 400  2 200  1 950  1 350  1 650  1 000  1 250  1 000  2 550  12.8 
30,000  2 800  2 550  2 250  1 550  1 900  1 250  1 750  1 250  2 900  9.7 
40,000  3 100  2 800  2 500  1 800  2 100  1 500  2 200  1 500  3 150  7.9 
50,000  3 350  3 050  2 750  2 000  2 300  1 700  2 600  1 650  3 400  6.8 
100,000  4 250  4 000  3 750  3 000  3 400  2 400  4 550  2 250  4 300  4.3 
150,000  5 000  4 850  4 600  3 850  4 450  2 850  6 200  2 500  5 000  3.3 
200,000  5 750  5 650  5 400  4 550  5 350  3 200  7 800  2 650  5 600  2.8 
300,000  7 250  7 250  6 850  5 550  6 750  3 700  10 600  2 800  6 650  2.2 
500,000  10 150  10 050  9 250  7 000  8 600  4 250  . .  2 800  8 350  1.7 
1,000,000  15 100  15 250  13 200  8 900  10 950  4 850  . .  . .  11 750  1.2 
2,000,000  20 350  22 550  17 700  10 600  12 700  . .  . .  . .  17 050  0.9 
5,000,000  25 900  36 100  23 900  11 900  13 250  . .  . .  . .  28 450  0.6 
10,000,000  27 750  49 750  27 950  . .  . .  . .  . .  . .  37 950  0.4 
15,000,000  . .  . .  . .  . .  . .  . .  . .  . .  42 850  0.3 

. . not applicable 